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Question

# The area of an isosceles triangle ABC is 48 cm2, where AB = AC. If the perimeter of the triangle and its altitude AD on BC are 32 cm and 8 cm respectively, then the length of the equal sides is equal to

A
8 cm
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B
10 cm
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C
12 cm
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D
13 cm
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Solution

## The correct option is B 10 cm Area of ΔABC=12×Base×Altitude ⇒48=12×BC×AD ⇒48×2=BC×8 (∵AD=8cm) ⇒BC=12cm …..(i) Perimeter of ΔABC=32cm ⇒AB+BC+AC=32 ⇒2AB+12=32 (∵AB=AC and BC=12cm) ⇒AB=32−122=10cm Thus, the length of the equal sides of ΔABC is 10 cm. Hence, the correct answer is option (b).

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